Lattices embeddable in three-generated lattices
We prove that every finite lattice L can be embedded in a threegenerated finite lattice K. We also prove that every algebraic lattice with accessible cardinality is a complete sublattice of an appropriate algebraic lattice K such that K is completely generated by three elements. Note that ZFC has a...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2016
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| Sorozat: | Acta scientiarum mathematicarum
82 No. 3-4 |
| Kulcsszavak: | Rácsok, Schmidt Tamás, Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-015-586-2 |
| Online Access: | http://acta.bibl.u-szeged.hu/46316 |
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| 024 | 7 | |a 10.14232/actasm-015-586-2 |2 doi | |
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| 245 | 1 | 0 | |a Lattices embeddable in three-generated lattices |h [elektronikus dokumentum] / |c Czédli Gábor |
| 260 | |a Bolyai Institute, University of Szeged |b Szeged |c 2016 | ||
| 300 | |a 361-382 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 82 No. 3-4 | |
| 520 | 3 | |a We prove that every finite lattice L can be embedded in a threegenerated finite lattice K. We also prove that every algebraic lattice with accessible cardinality is a complete sublattice of an appropriate algebraic lattice K such that K is completely generated by three elements. Note that ZFC has a model in which all cardinal numbers are accessible. Our results strengthen P. Crawley and R. A. Dean's 1959 results by adding finiteness, algebraicity, and completeness. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Matematika | |
| 695 | |a Rácsok, Schmidt Tamás, Matematika | ||
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/46316/1/math_082_numb_003_004_361-382.pdf |z Dokumentum-elérés |